The thermoelectric (TE) effect refers to phenomena in which a temperature difference creates an electric potential, or an electric potential creates a temperature difference. Therefore, a thermoelectric device creates a voltage when there is a different temperature imposed on opposing sides of the device or, when a voltage is applied across it, the device creates a temperature difference.
A thermoelectric material is a material that shows a strong thermoelectric effect. The performance of thermoelectric materials used in thermoelectric devices is measured using the dimensionless figure-of-merit ZT=S2σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the temperature in Kelvin. Since S is a fundamental material property that also affects the electrical conductivity, most attempts on increasing ZT have focused on enhancing σ and/or suppressing κ. Since electrons conduct both heat and electricity, it has proven to be a difficult task to ensure the increase in σ at the expense of κ.
The efficiency of thermoelectric devices is dependent on several materials properties. As described above, it can be quantified by the dimensionless thermoelectric figure-of-merit, ZT. One of the most promising approaches for bulk thermoelectric materials preparation is to create highly doped, small band-gap semiconductors. The problem is that the three parameters in ZT (S, σ, and κ) are not independent. In general, as S increases, σ decreases. The best compromise seems to be using heavily doped semiconductors to produce a carrier density of about 1019/cm3. Furthermore, κ has two contributions, one from the electrical carriers, κe, and one from the lattice vibrations (phonons), κph. Although κe is proportional to σ, in many semiconductors κph is much greater than κe, so that the major challenge, short of changing the material, is to minimize κph.
In the standard model of semiconductor transport, it can be shown that ZT is a monotonically increasing function of two parameters: EG and B, where EG is the band gap and B is determined by a number of materials parameters. See A. S. Henry and G. Chen, J. Computational and Theoretical Nanoscience 5, 1 (2008). In this analysis, it is assumed that the semiconductor carrier density (n- or p-type) has been adjusted by doping to the optimal level. Then, the band gap EG must be greater than kT (the thermal energy) by a factor of about 10 to maximize ZT for a given B. B is a product of several factors: B˜Nv μm3/2/κph. Nv is the degeneracy of the band extrema near the Fermi level, μ is the electronic mobility, and m is the band mass determined by the density of states. Each parameter can be considered in turn. The crystalline symmetry limits the maximum value of Nv, and it attains its maximum value in cubic space groups (in which case it might be as high as 48). For high ZT, the electronic mobility μ should be high, but generally, the mobility and the band mass m are not independent. The mobility is inversely proportional to the band mass in the direction of the current flow, mi, according to: μ=eτ/mi, where τ is the carrier scattering time. Thus, B is proportional to Nvτ(m)3/2/miκph. In noncubic materials, mi can be different from m. In that case, when m>mi, B is increased. However, exploiting an anisotropic mass may run counter to increasing Nv, so a compromise must be struck. Interestingly, the current TE materials all have cubic or hexagonal symmetry. Finally, long scattering times are possible if the electronegativity differences between the elements in the material are small and optical vibrations have small coupling to the carriers. The latter condition is difficult to control or design, but small coupling is favored if the each atom has a large number of near neighbors, say six or greater.
Most current high-ZT research efforts focus on reducing the thermal conductivity in semiconductor materials with favorable Seebeck coefficients while enhancing electrical conductivity, and can be broadly categorized by materials type as uniform bulk materials, compositionally modulated films, and nanostructured materials. With all of these material systems, the approach typically involves starting with a bulk material that either has a large electrical conductivity or that can be doped to increase the electrical conductivity of the material, and then reducing the thermal conductivity due to phonons as much as possible without impacting the electrical conductivity.
The simplest approach to a high-ZT material is to choose a conducting (or semiconducting) material that has a small thermal conductivity. Such materials tend to be compounds made from heavy elements, as the high atomic masses reduce the atomic vibration frequencies and hence the thermal conductivity (at room temperature and greater). However, the low vibration frequencies reduce the electrical conductivity as well. Other approaches include having a large number of atoms (N) in the unit cell of crystalline compounds or using alloys to prepare structurally complex materials. The large N lowers the fraction of vibrational modes (phonons) that carry heat efficiently (acoustic modes) to 1/N, whereas the disorder of random atomic substitution in an alloy scatters the phonons, which reduces the thermal conductivity. In both cases, the distance between the scattering centers can be difficult to control and may approach the mean free path of electrons in the material, reducing the electrical conductivity. See G. A. Slack, CRC Handbook of Thermoelectrics, Boca Raton, Fla.: CRC Press (1995). Thus, this approach is limited by the mechanisms that can be used to tune material properties, with essentially no capability for reducing the thermal conductivity independent of the electrical conductivity.
The compositionally modulated films used to create synthetic high-ZT materials generally fall into two categories: devices in which current and heat flow parallel to the layers, and ones in which both flow perpendicular to the layers. In the first approach, an increase in Z has been calculated to arise from a number of factors, including an increase in the electronic density of states per unit volume that consequently increases the thermopower that would occur for small well widths (several nanometers), as well as an increase in carrier mobility if modulation doping is exploited. See M. G. Holland, Physical Review 132, 2461 (1963). A potential difficulty in obtaining higher ZT from such devices is that the inert spacers used to separate the active layers of such structures do not contribute to heat flow, but have a thermal conductivity that increases the heat load and lowers the effective ZT of the overall device. The second approach has demonstrated a much more profound effect on phonon transport, either through phonon confinement or phonon scattering mechanisms, using layered structures that minimize the impact of the barrier layer on the electrical conductivity. However, these techniques rely on costly and time consuming growth fabrication processes, and often utilize materials that can be challenging to pattern or incorporate with standard microelectronics. See A. Balandin and K. L. Wang, Journal of Applied Physics 84, 6149 (1998); G. Chen, Physical Review B 57, 14958 (1998); and R. Venkatasubramanian, Physical Review B 61, 3091 (2000).
The nanostructured materials approach to increasing ZT also attempts to reduce thermal conductivity through boundary layer scattering, either by constraining the dimensionality of the material by creating structures such as nanowires and quantum dots, or using either random or periodic defects in a bulk TE material. In this approach, defects with length scales on the order of the mean free path of phonons in the bulk material are used to effectively scatter thermal phonons and thus reduce the thermal conductivity of the composite material. See C. Chiritescu et al., Science 315, 351 (2007); and R. Venkatasubramanian et al., Nature 413, 597 (2001). The method using low-dimensional structures such as nanowires have been shown to dramatically reduce the thermal conductivity versus bulk materials of the same composition by phonon drag in the highly-confined nanowire and phonon scattering from the boundaries of the structure. See A. I. Hochbaum et al., Nature 451, 163 2008; and J.-K. Yu et al., Nature Nanotechnology, advance online publication 2010. Despite the impressive ZT values of such structures, they are impractical from a device point of view due to the inherent small usable material area and structural fragility of such topologies. Attempts to alleviate these issues with nanomeshes and arrays of nanowires result in only modest improvements in the structural integrity at best. The random defect approach has demonstrated significant thermal conductivity reduction without the need for complicated fabrication techniques and without removing a large fraction of the bulk solid area, but with limited degrees of freedom to optimize the effect besides rough control of the defect size and density. See C. Chiritescu et al., Science 315, 351 (2007).
Therefore, a need remains for a thermoelectric material that has a large Seebeck coefficient, high electrical conductivity, and low thermal conductivity and can be fabricated into devices using techniques that are compatible with standard microelectronics.